The slip line fields proposed by Hillier in this paper are inadmissible since the stress fietds cannot be extended into the rigid region at point 00' without violating the yield criterion. The stresses on the non deforming region in the neighbourhood of point 00' are as shown in the figure. It may be shown from the well known inequalities due to Hill ~) that these stresses violate the yield criterion. It is interesting to note, however, that if the direction of the shearing stress k is reversed, the wedge does not yield.
00'
For plane strain indentation with a flat punch the Prandtl solution is valid for any frictional condition since there is no relative movement between the puneh and the metal. The Hill solution ean be realized approximately in experiments if certain lubricants are used. The squeezing out of the lubricallt produees a small shearing traction on the metal at the contaet area and this traction is directed outwards. This results in a velocity field similar to Hill's field.
Yield loads obtained from the Prandtl solution are in good agreement with experimental results for indentation with rough punches whereas indenration loads from Hillier's so]ution are not.